Extensions of a tight function and their continuity in quantum logic
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In the present paper, a new variation of a nonnegative real-valued function \(\rho \) defined on a subfamily of a quantum logic P is proposed, and the notion of tightness of \(\rho \) is studied. Various crucial results are proved, and subsequently we have obtained extensions, viz. f-extension, \(\delta \)-extension and \(\sigma \)-extension of a tight function \(\rho ;\) continuity of extensions of \(\rho \) with respect to an approximating family in P is discussed.
KeywordsOrthomodular lattices Continuity Tight functions Approximating families
The authors are grateful to the anonymous referees for their valuable suggestions toward the improvement of the paper.
The second author acknowledges with gratitude the financial support by Department of Science and Technology (DST), New Delhi, India, under INSPIRE fellowship No. IF160721.
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Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent was obtained from all individual participants (co-author) included in the study.
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